Question

A diamond weighs 3.71 g. It is put into a box weighing 1.4kg. Find the total weight of the box and diamond to the correct number of significant figures.

Answer 1

Hint: We need to add the given diamond mass and the mass of the box in the normal way and then find the value up to two significant digits by rounding the digits after the decimal point depending on the value of the digit if less or greater than 5.

Complete step-by-step answer:
Given the weight of the diamond = 3.71 g
We know the conversion between the grams and kilograms is 1kg = 1000g
So the value of the weight of the diamond in kgs becomes: 3.71 $\times10 ^{-3}$ = 0.00371 kg
Given Weight of the box = 1.4 kg
Therefore total weight = weight of the diamond + weight of the box
Now the value of the total weight in kgs becomes: 1.4 + 0.00371 = 1.40371 kg
Now we have found the value of the total weight in kgs so we get the value up to 2 significant digits by rounding the digits as 1.4 kg as the value after 4 is 0 which Is less than 5. So we have taken the number before 0 as it is.
So we have found the value of the total weight in kgs up to correct significant digits by
Hence the correct value of the weight of the total weight up to 2 significant digits is 1.4 kg

Additional information:
The correct number of the significant digits are found by taking the least number of significant digits present in the given numbers. For example, in the above problem, we have the number 1.4 kg which has the least number of significant digits equal to 2. Hence we need to find the sum or subtraction normally and then round off the digits up to the least number of the significant digits present in the given numbers.

Note: One of the possible mistakes that usually one tends to make in this kind of problem is that we take the number of significant digits as 3 thinking that 3.71 g has three significant digits and the answer goes wrong. We need to understand here that we need to take the correct number of significant digits as the least number of significant digits present in the given numbers after converting them into the same units.